There are definitely competing factors going on when you consider ring thickness. The "good" side of a tree is the side that felt some tension when growing, and that is generally the side with thinner rings. You get some nice reflex out of those kind of staves. So as long as the spring/summer ratio is decent, it is likely to perform better for this reason.
Making bendy handle bows is a good way to lower stress too, you don't have those nasty fades to try and tiller and in general you wind up with more working wood per limb even though it might bend a little harder since its shorter.
I'm not trying to discourage anyone from making a bow out of a piece of hedge. I'm all for using what you have, and an average piece of hedge can make an above-average bow. That particular blank has a nice dense looking outer 1/8", plus a couple of denser looking sections in between some of the lighter looking stuff. If you could possibly design it so the denser loking stuff was on the exterior of both back and belly, it wouldn't matter what the middle section looked like.